Parallel mobile coil mechanism for magnetic manipulation in large workspace

ABSTRACT

A magnetic manipulation system and method for moving and navigating a magnetic device in a body are provided. The system includes a robotic parallel mechanism having at least three electromagnets and at least three electromagnetic coils coupled to the at least three electromagnets, respectively. The electromagnetic coils are actuated to keep the electromagnets in static conditions or move the electromagnets along a desired trajectory, a current control unit supplying currents to the electromagnetic coils which have soft iron cores. The currents supplied by the control unit are configured to generate dynamic magnetic field in the soft iron core&#39;s linear region. The current control unit and the robotic parallel mechanism are configured to generate desired dynamic magnetic fields in desired positions within a workspace to control a magnetic device, and a three-dimensional position sensor is configured for performing a close loop control of the robotic parallel mechanism.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application Ser.No. 63/040,057, filed Jun. 17, 2020, which is hereby incorporated byreference in its entirety including any tables, figures, or drawings.

BACKGROUND OF THE INVENTION

Untethered small-scale magnetically actuated devices have been an activeand attracted research field during last two decades. These devicestypically consist of some forms of mechatronic or microelectromechanical systems (MEMS) devices with a rigidly attachedmagnetic body on which magnetic forces and torques are applied by anexternal field. Their great potential in minimally invasivesurgery/medicine has been widely noticed due to the intrinsic advantagesof magnetic field, such as high safety to living organisms and goodcontrollability. Compare to traditional endoscopy, using magneticcapsule endoscopes in diagnosing diseases in the gastrointestinal tractreduces the examination time and retention rate. Actively controlledcapsule endoscopy would also allow the examination of the entiregastrointestinal (GI) tract. For vascular diseases, endovascularinterventions using magnetic catheters have advantages over traditionalmanual techniques in terms of accuracy and surgical or diagnosticduration.

To actuate and control the aforementioned magnetic medical devices,various magnetic manipulation systems generating magnetic torque and/ormagnetic force are proposed. Some approaches utilize magnetic forces forpulling while others apply torques generated by rotating magnetic fieldsto roll on a surface, travel through a fluid, crawl through a lumen viahelical propulsion, or screw through soft tissues. These systems adopteither electromagnetic coils or permanent magnets for field generation.Using multiple stationary electromagnetic coils, systems with differentconfigurations have been developed for magnetic manipulation. Helmholtzor near-Helmholtz coils and their combinations with Maxwell coils aremost commonly used. Towards specific applications, researchers havedeveloped custom stationary magnetic manipulation systems for bothminimally invasive operation and micro robotic research. However, whenfacing a requirement of a large workspace (for example, with the humanbody size), the limitations of this type of design using stationarycoils emerge. The large coil size and heavy weight may lead to highercomplexity on the structural design and fabrication. Increasedinductance of the enlarged coil limits the control bandwidth of theeffective magnetic field.

Alternative methods employ permanent magnets to create dynamic magneticfields. However, due to large inertia and limited motion range of thepermanent magnets, this kind of system has low control bandwidth. Fortackling the problems of scalability and control bandwidth, systems withmobile permanent magnets provide a solution. Owning to the strongmagnetic field and compact size, a single permanent magnet can becarried by a human hand or a serial robotic manipulator to reach a largeworkspace. Its magnetic field is controlled by adjusting the positionand pose of the magnet. Considering that control of the magnetic fieldgenerated by permanent magnets is a challenging task, there may besafety concerns in applications since the field of permanent magnetscannot be switched off.

Although electromagnetic coils and permanent magnets generate equivalentmagnetic fields, coils have often been the preferred choice due to theirabilities to easily control the field by regulating the coil currentsand to completely turn off the field. Concepts of magnetic manipulationusing several mobile coils were proposed. The advantages of this type ofsystem are revealed compared to stationary coil systems and permanentmagnet systems. However, up to now, only one-dimensional (1D) rotationand planar motion of coils were realized. Two main challenges hinder therealization of three-dimensional (3D) motion of multiple coils. On onehand, large sizes and weights of the coils, which are utilized togenerate a strong magnetic field, brings in the design complexity of thepositioning mechanism. On the other hand, position and pose variationsof multiple coils lead to challenges in computing the resultingcomposite field in real time.

BRIEF SUMMARY OF THE INVENTION

There continues to be a need in the art for improved designs andtechniques for a system for manipulating and guiding small-scalemagnetically actuated devices for clinical applications.

Embodiments of the subject invention pertain to a magnetic manipulationsystem having mobile coils for moving and navigating a magnetic devicein a body.

According to an embodiment of the subject invention, the magneticmanipulation system comprises a robotic parallel mechanism comprising atleast three electromagnets and at least three electromagnetic coilscoupled to the at least three electromagnets, respectively, wherein theelectromagnetic coils are configured be actuated to keep theelectromagnets in static conditions or move the electromagnets along adesired trajectory; a current control unit supplying currents to theelectromagnetic coils, the electromagnetic coils having soft iron cores,wherein the currents supplied by the control unit is configured togenerate dynamic magnetic field in the soft iron core's linear region,wherein the current control unit and a robotic parallel mechanism areconfigured to generate desired dynamic magnetic fields in desiredpositions within a workspace to control a magnetic device; and athree-dimensional (3D) position sensor is configured for performing aclose loop control of the robotic parallel mechanism. The magneticmanipulation system may further comprise a coil-end joint plate,actuation units and structural linkages that connect the coil-end jointplate to the robotic parallel mechanism. The coil-end joint plate has aplurality of sides corresponding to a plurality of branches of eachelectromagnetic coil; wherein instruments are mounted on the coil-endjoint plate and the coil-end joint plate is connected to the lower endof every electromagnetic coil. The robotic parallel mechanism is anactuation mechanism of K branches including linear actuation mechanismsand rotational actuation mechanisms, wherein K is an integer greaterthan zero, and wherein the rotational actuation mechanisms includemotors and gears, motors and belts, or motors and linkages; and whereinthe linear actuation mechanisms include ball screw tables, sliding trackand pneumatic actuation. The robotic parallel mechanism is made of lowmagnetic permittivity materials including aluminum and 304 steel. Aposition of a center of the coil-end joint plate has a deterministicrelationship with actuator positions of the robotic parallel mechanismwhile an orientation of the coil-end joint plate is constrained by therobotic parallel mechanisms to be invariant. The coil-end joint plate isconfigured to install one or more instruments selected from 3Dultrasonic probes, 3D magnetic sensors or stereo cameras, the 3Dultrasonic probes, the 3D magnetic sensors and the stereo cameras beingmodulated and interchangeable. A 3D location method is configured toconduct close loop control of a plurality of magnetic objects, andwherein the 3D location method includes one or more selected fromultrasonic imaging, magnetic localization, and vision-based localizationmethod, depending on the instruments installed on the coil-end plate.The electromagnetic coils are connected to the coil-end joint plate byuniversal joints, and wherein the electromagnetic coils move and arealigned with the structural linkages. The magnetic manipulation systemcan further comprise an isolation plate attached to the coil-end jointplate for controlling a distance between the magnetic manipulationsystem and the body that includes magnetically controlled objects andintegrates distance sensors and temperature sensors to inhibit bodycollision and overheating.

In another embodiment, a method of a magnetic manipulation system havingmobile electromagnetic coils for moving and navigating a magnetic devicein a body is provided. The method determines parameters of the magneticmanipulation system to keep the magnetic manipulation system as compactas possible and inhibit any singularities with respect to bothkinematics and field generation. The method can comprise analyzing aworkspace of the magnetic manipulation system; determining spatialrelationships between coil branches of the magnetic manipulation systemand actuation mechanisms of the coil branches; and determining optimallink length of the coil branches. The method can further compriseoptimizing for deriving the optimal link length, wherein performancemetrics for motion actuation and field generation are evaluated based ona condition number of the performance metrics. The workspace isaxis-symmetric and a bottom center of the workspace is located on asymmetry axis of the workspace. The spatial relationship between thecoil branches and the moving trajectories of the coil branches isdelimited by the singularities and physical constraints of the magneticmanipulation system. The link length is optimized based on minimumradius of the magnetic manipulation system and whether there is enoughspace for hardware implementation. The method can further compriseproviding a framework for calculating and controlling field generationof the coil branches of the magnetic manipulation system, wherein theframework includes a field map of a one or more of the coil branches,inverse kinematics of the coil branches and field computation andcontrol by dynamic coordinate transformation. The method can furthercomprise generating and calibrating a unit map of one of the coilbranches; wherein the coil branches each has a length-to-diameter ratiogreater than 3, a field map domain greater than twice of a diameter ofthe corresponding coil branch and a distance between the correspondingcoil branch and the field map domain smaller than one half of a lengthof the corresponding coil branch; wherein a neural network is utilizedto calibrate finite element data created by a simulation of the fieldmap domain of the corresponding coil branch; wherein real magnetic fieldvectors which are experimentally measured at data points are based on tocalibrate a 3D magnetic field map and the magnetic field gradient. Themethod can further comprise providing currents to the coil branches forgenerating desired magnetic field, which comprises deriving the inversekinematics of the coil branches and field computing and controlling bythe dynamic coordinate transformation; wherein the magnetic fieldcalculation and the field superposition of the coil branches isperformed by the dynamic coordinate transformation and a unit map of oneof coil branches; wherein the resulting magnetic field vectors and thegradient matrices connect the currents the coil branches that iscontrollable to a desired magnetic field.

In certain embodiment, an interchangeable coil assembly can comprise acore, a coil frame, and a coil. The coil frame decouples the coil andthe core, and either of the part is changed when the other one fails,and different core tips are configured to be inserted in the coil frameto meet magnetic field requirements. The interchangeable coil assemblycan further comprise a cooling unit for controlling temperature of thecoil, and the temperature control unit monitoring the coil temperaturethrough thermal sensors and regulating the heat exchange rate to keepthe coil in a suitable working condition and elongate continuous workingtime of the interchangeable coil assembly.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention are described in the followingwith reference to the drawings, which are for the purpose ofillustrating the present preferred embodiments of the invention and notfor the purpose of limiting the same. In the drawings,

FIG. 1 is a schematic representation illustrating a magneticmanipulation system having mobile parallel electromagnetic coils,according to an embodiment of the subject invention.

FIG. 2 is a geometric representation of one branch of the mobileparallel coil mechanism, according to an embodiment of the subjectinvention.

FIGS. 3A-3B show unit field maps of the mobile parallel coils andcalibration results of the mobile parallel coils, respectively,according to an embodiment of the subject invention.

FIG. 4 is a schematic representation illustrating the plane expanded bya symmetry axis of the workspace and the k^(th) sliding track, accordingto an embodiment of the subject invention.

FIG. 5 shows plot diagrams of performance simulation results with K=3and θ=0° for different coil branch lengths, according to an embodimentof the subject invention.

FIGS. 6A-6B are plot diagrams of performance metrics of the wholeworkspace, according to an embodiment of the subject invention.

FIG. 7 shows results of field generation performance for the optimizedcoil branch length L_(opt) when the relative position between thecoil-end plate and the magnetic device varies, according to anembodiment of the subject invention.

FIGS. 8A-8C are schematic representations illustrating the mechanicaldesign of the magnetic manipulation system, which includes thecoil-branch and the coil-end plate, according to an embodiment of thesubject invention.

FIG. 9 is a block diagram of the magnetic manipulation system, accordingto an embodiment of the subject invention.

FIGS. 10A-10C are schematic representations illustrating three differentmobile parallel coil mechanism, according to an embodiment of thesubject invention.

FIGS. 10D-10F shows experimental results of the field generation of thethree mobile parallel coil mechanism of FIGS. 10A-10C, respectively, thereference fields for the three mobile parallel coil mechanism being setas circular rotating fields on XY, YZ and XZ planes, respectively,according to an embodiment of the subject invention.

FIGS. 11A-11F shows alternative actuation systems and methods fordifferent applications, wherein FIGS. 11A-11C show alternative actuationsystems and methods with various rotational joints and FIGS. 11A-11Cshow alternative actuation systems and methods with various linearactuations, according to an embodiment of the subject invention.

FIGS. 12A-12D are schematic representations illustrating theinterchangeable coil assembly and coil connection methods, according toan embodiment of the subject invention.

FIGS. 13A-13D are schematic representations illustrating various coiltip shapes, according to an embodiment of the subject invention.

FIGS. 14A-14B are schematic representations illustrating an isolationplate, according to an embodiment of the subject invention.

DETAILED DISCLOSURE OF THE INVENTION

The presented invention relates to a magnetic manipulation andnavigation system comprising at least three electromagnetic coils formoving and navigating magnetic devices in or through a body of a livingcreature. Such a body may have a cavity comprising liquid or softtissues and a magnetic device to be displaced inside the cavity.Electromagnetic coils are structured in a parallel mechanism and canmove to predetermined positions in the vicinity of the body.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the term “and/or” includes any and all combinations of oneor more of the associated listed items. As used herein, the singularforms “a,” “an,” and “the” are intended to include the plural forms aswell as the singular forms, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, steps, operations, elements, and/orcomponents, but do not prelude the presence or addition of one or moreother features, steps, operations, elements, components, and/or groupsthereof.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by onehaving ordinary skill in the art to which this invention pertains. Itwill be further understood that terms, such as those defined in commonlyused dictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art and thepresent disclosure and will not be interpreted in an idealized or overlyformal sense unless expressly so defined herein.

When the term “about” is used herein, in conjunction with a numericalvalue, it is understood that the value can be in a range of 90% of thevalue to 110% of the value, i.e. the value can be +/−10% of the statedvalue. For example, “about 1 kg” means from 0.90 kg to 1.1 kg.

While these exemplary embodiments are described in sufficient detail toenable those skilled in the art to practice the invention, it should beunderstood that other embodiments may be realized and that variouschanges to the invention may be made without departing from the spiritand scope of the present invention. Thus, the following more detaileddescription of the embodiments of the present invention is not intendedto limit the scope of the invention, as claimed, but is presented forpurposes of illustration only and not limitation to describe thefeatures and characteristics of the present invention, to set forth thebest mode of operation of the invention, and to sufficiently enable oneskilled in the art to practice the invention. Accordingly, the scope ofthe present invention is to be defined solely by the appended claims.

Referring to FIG. 1, a magnetic manipulation system comprises aplurality of, for example three, mobile electromagnetic coils and arobotic parallel mechanism for controlling one or more magnetic devicesnavigating the body. The body can be viewed as a cavity comprisingworkspace filled with liquid or air. The plurality of, for examplethree, mobile electromagnetic coils is actuated by parallel mechanismsto realize a large effective 3-dimensional workspace of the body.

Desired magnetic fields for manipulation of the magnetic devices areachieved by controlling electrical currents of the plurality ofelectromagnetic coils. The manipulation is realized by localization ofthe magnetic devices using sensors so that the energy consumption andheat generation are reduced.

In one embodiment, an implementation of high-resolution localizationsensors is realized for easy eye-in-hand configuration. The employmentof the plurality of electromagnetic coils makes it safe for the humanbody since the magnetic fields can be easily switched off. The magneticdevices such as magnetic capsules are positioned in the body andcontrolled by the magnetic field generated by the mobile electromagneticcoils.

In one embodiment, the magnetic manipulation system can comprise anynumber of electromagnetic coils and a shape of the coil-end joint platemay vary. By performing the actuation method of the magneticmanipulation system, the electromagnetic coils can move to desiredlocations within the working space of the body.

Large workspace is ensured by the mobility of the parallel-roboticstructure. The magnetic manipulation system is highly accessible becausethe mobile electromagnetic coils only take a part of the workspace. Whenthe system is turned on, the robotic parallel structure can either staystatic to keep the electromagnetic coils in a predetermined position ormove along a desired trajectory. The current supply unit, workingtogether with the parallel coil actuation method, controls the currentof the coils to generate desired dynamic magnetic field.

In one embodiment, the magnetic manipulation system comprises Kelectromagnetic coils, each of which is actuated by a linear actuatorthat moves on a fixed track as shown in FIG. 1, wherein K is a positiveinteger value. The other ends of the electromagnetic coils aresymmetrically attached to the coil-end plate via connections such asball joints. With this configuration and the assumption that orientationof the coil-end plate is constrained to be invariant, the position ofthe center of the coil end plate (

∈

) has a unique deterministic relationship with the actuator positions(q=[q₁ q₂ . . . q_(K)]^(T)∈

^(K)) shown by Equation (1):

=

(q)  (1)

where {

} denotes the global coordinate frame.

It is noted that the inverse of equation (1), i.e. q=

⁻¹(

), exists, which represents the inverse kinematics of the parallelmethod. The position of a working point (P_(w)∈

³) expressed in the local reference frame—{

} of the k-th coil is

∈

³, and the coordinate transformation is defined by Equation (2):

=

(

,

)  (2)

Due to the varied position and pose of the coil relative to the coil-endplate and nonlinearity of

(q),

(

,

) is a series of nonlinear transformation functions.

When the k^(th) coil with a soft iron core is operated in its linearrange, its magnetic field (

∈

³, unit: mT) and gradient matrix (

∈

^(3×3), unit: mT/m) at

depend linearly on the coil current (i_(k)) and are given by Equation(3):

$\begin{matrix}\left\{ \begin{matrix}{{h_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)} = {{{\mathcal{i}}_{k} \cdot {{\overset{\_}{h}}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}} = {{\mathcal{i}}_{k} \cdot {{\overset{\_}{\mathcal{M}}}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}}} \\{{G_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)} = {{{\mathcal{i}}_{k} \cdot {{\overset{¯}{G}}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}} = {{\mathcal{i}}_{k} \cdot \left( {\frac{\partial{\mathcal{M}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial x^{\mathcal{C}_{k}}}\frac{\partial{\mathcal{M}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial y^{\mathcal{C}_{k}}}\frac{\partial{\mathcal{M}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial z^{\mathcal{C}_{k}}}} \right)^{T}}}}\end{matrix} \right. & (3)\end{matrix}$

where

(·) stands for the unit field map of the k^(th) coil at its local frame.After coordinate transformation, the magnetic field in the globalcoordinate frame is obtained by Equation (4):

(

)=

(

,

)·

(

)  (4)

where

(

,

)∈

^(3×3) is the corresponding rotation matrix for the k-th coil.

There are two types of control methods for the magnetic devices: amagnetic torque control method and a magnetic force control method. Fordevices that are controlled by the magnetic torque method (for example,microrobots moving in liquid that align with orientation of magneticfield), the device control method is essentially based on a magneticfield control method. According to the superposition property ofmagnetic fields and assuming that the magnetic field of a coil is in alinear relationship with the coil current, the total field at

is computed by Equation (5):

=[

. . .

]·i=H·i  (5)

where i=[i₁ i₂ . . . i_(K)]^(K)∈

^(k) is the vector of coil currents. If a desired field is given and Hdoes not have singularity, the exact required coil currents can beobtained by Equation (6):

i=H ^(†)·

  (6)

where H ^(†) represents the general inverse of H.

Unlike the torque control method, the force control method requires adifferent computation process because the gradient matrix isnon-rotational. To solve this problem, the unit magnetic forces at thelocal frames are first calculated by Equation (7):

$\begin{matrix}{{{\overset{\_}{f}}^{\mathcal{C}_{k}}\left( {p_{W}^{\mathcal{C}_{k}},m^{\mathcal{G}}} \right)} = {{{{\overset{\_}{G}}_{k}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)} \cdot m^{\mathcal{C}_{k}}} = {{{\overset{\_}{G}}_{k}^{\mathcal{G}}\left( p_{W}^{\mathcal{C}_{k}} \right)} \cdot {{{}_{}^{\mathcal{C}k}{}_{}^{}}\left( {p_{W}^{\mathcal{G}} \cdot p_{P}^{\mathcal{G}}} \right)} \cdot m^{\mathcal{G}}}}} & (7)\end{matrix}$

where

∈

³ is the magnetic moment of the controlled magnetic device, and

=

. Then, the unit magnetic forces are transformed to the globalcoordinate frame by Equation (8):

=

·

  (8)

According to the superposition principle, the total magnetic force at

is computed by Equation (9):

=[

. . .

]·i=F·i  (9)

Finally, if a desired force is given and F does not have singularity,the exact required coil currents can be obtained by Equation (10)

i=F ^(†)·

  (10)

FIG. 2 is a geometric representation of one branch of theparallel-mobile-coil mechanism. The parallel mobile coil comprises Kbranches having a rotationally symmetric distribution around

. Accordingly, the instrument connected to the parallel mobile coil hasK sides to locate the robotic parallel links and the coils.

With two constraints on the mechanical design that the normal vector ofthe coil end plate—

, is in parallel to

and the normal vector of the sliding surface of the linear actuator—

is perpendicular to

.

In one embodiment, the magnetic manipulation system of FIG. 1 has threebranches, wherein the parallel kinematics can be derived. Nevertheless,the value of θ can be flexibly chosen for specific applicationscenarios. The type of parallel actuated mechanism of FIG. 2 can also berotational mechanisms or any other parallel mechanism as long as theactuators fulfill the requirements of the parallel mechanism.

All electromagnetic coils comprise soft iron cores and are connected tocoil-end plate by universal joints as shown in FIG. 1. Triangular-shapedinstrument plate which corresponds to the number of coils can be used.Universal joints may also be ball joints or other types of two degree offreedom (DOF) joints that allow the parallel movement of the roboticstructure.

The inverse kinematics that is necessary for the closed-loop control ofthe parallel-mobile-coil mechanism is derived as below. Coordinates ofall the points are computed with respect to the global coordinate frame{

−

}. As shown in FIG. 2, points P and W denote the positions of thecoil-end plate and the magnetic device, respectively. Their coordinatesare expressed by

=[x_(p), y_(p), z_(p)]^(T) and

=[x_(W) y_(W) z_(W)]^(T)·q_(k) stands for the position of the k^(th)(k=1, 2, . . . , K) linear actuator moving from a top home position. Bythe mechanism design, coordinates of M_(k) are calculated by Equation(11):

$\begin{matrix}{p_{M_{k}}^{\mathcal{G}} = {\begin{bmatrix}x_{M_{k}} \\y_{M_{k}} \\z_{M_{k}}\end{bmatrix} = \begin{bmatrix}{x_{P} + {L_{MP}{\cos\left( \alpha_{k} \right)}}} \\{y_{P} + {L_{MP}{\sin\left( \alpha_{k} \right)}}} \\z_{P}\end{bmatrix}}} & (11)\end{matrix}$

where L_(MP) is a constant length between point P and point M_(k), andα_(k) is defined by Equation (12):

$\begin{matrix}{\alpha_{k} = {\frac{360{^\circ}}{K}\left( {k - 1} \right)}} & (12)\end{matrix}$

Similarly, coordinates of A_(k) are obtained by Equation (13):

$\begin{matrix}{p_{A_{k}}^{\mathcal{G}} = {\begin{bmatrix}x_{A_{k}} \\y_{A_{k}} \\z_{A_{k}}\end{bmatrix} = \begin{bmatrix}{\left( {L_{h} + {q_{k}{\sin(\theta)}}} \right){\cos\left( \alpha_{k} \right)}} \\{\left( {L_{h} + {q_{k}{\sin(\theta)}}} \right){\sin\left( \alpha_{k} \right)}} \\{L_{V} - {q_{k}{\cos(\theta)}}}\end{bmatrix}}} & (13)\end{matrix}$

where L_(h) and L_(V) stand for the horizontal distance and verticaldistance between

and A_(k) when q_(k)=0, respectively. From the mechanical constraint, ∥

∥ is a constant, as shown in Equation (14):

∥

∥−L _(AM)=0  (14)

By Eq. (10)-(13), the inverse kinematics of the parallel-mobile-coilmechanism is obtained by Equation (15):

$\begin{matrix}{q_{k} = {{\mathcal{F}^{- 1}\left( p_{P}^{\mathcal{G}} \right)} = \left\{ \begin{matrix}{{C_{1} - \sqrt{C_{1}^{2} - C_{2}}},} & {{0{^\circ}} \leq \theta \leq {45{^\circ}}} \\{{C_{1} + \sqrt{C_{1}^{2} - C_{2}}},} & {{45{^\circ}} \leq \theta \leq {90{^\circ}}}\end{matrix} \right.}} & (15) \\{Where} & \; \\\left\{ \begin{matrix}{C_{1} = {{\left( {{x_{P}\cos\;\alpha_{k}} + {y_{P}\sin\;\alpha_{k}} - L_{h} + L_{MP}} \right)\sin\;\theta} +}} \\{\left( {L_{V} - z_{P}} \right)\cos\;\theta} \\{C_{2} = {x_{P}^{2} + y_{P}^{2} + \left( {z_{P} - L_{V}} \right)^{2} + \left( {L_{h} - L_{MP}} \right)^{2} - L_{AM}^{2} -}} \\{2\left( {L_{h} - L_{MP}} \right)\left( {{x_{P}\cos\;\alpha_{k}} + {y_{P}\sin\;\alpha_{k}}} \right)}\end{matrix} \right. & (16)\end{matrix}$

With the inverse kinematics, the actuators' movements can be controlledto actuate the coil-end plate to the desired location

.

Due to the variation of the coil positions and poses, field and forcecomputations for every coil in the local frames and the field and forcesuperpositions of multiple coils in the global frame require dynamiccoordinate transformations:

transforms the global position of the working point to its position inthe local coordinate frame of the k^(th) coil and

transforms the magnetic field of k^(th) coil in its local coordinateframe to the global coordinate frame for the field superposition.Moreover,

transforms the magnetic moment of the device in the global frame to thecorresponding magnetic moment in the local frame of the k^(th) coil forforce computation.

In the global coordinate frame, for the k^(th) coil, the origin O^(C)^(k) of its local frame coincides with point C_(k) (as shown in FIG. 2and FIGS. 3A-3B). The coordinate of C_(k) is obtained by Equation (17):

$\begin{matrix}{p_{C_{k}}^{\mathcal{G}} = {\begin{bmatrix}x_{C_{k}} \\y_{C_{k}} \\z_{C_{k}}\end{bmatrix} = {p_{A}^{\mathcal{G}} + {\frac{L_{AC}}{L_{AM}}\left( {p_{M_{k}}^{\mathcal{G}} - p_{A_{k}}^{\mathcal{G}}} \right)}}}} & (17)\end{matrix}$

where L_(AC) and L_(AM) are constant lengths between A_(k) and C_(k) andbetween A_(k) and M_(k), respectively.

denotes the vector from point A_(k) to point C_(k), as shown in Equation(18):

=

−

  (18)

Since vectors

,

and

are coplanar, the following function holds as shown in Equation (19):

|

|=0  (19)

where

is defined by the same way as

, and |·| stands for the determinant operation. To simplify thecomputation, the local frame {C_(k)} is uniquely determined by twoconditions: 1) its {circumflex over (x)}^(C) ^(k) {circumflex over(z)}^(C) ^(k) plane coincides with the plane expanded by the threevectors in Equation (19); 2) its {circumflex over (x)}^(C) ^(k)direction is chosen such that x_(W) ^(C) ^(k) is always greater than orequal to 0. Based on the two conditions, in the local frame of thek^(th) coil, the coordinates of W read as shown in Equations (20)-(22):

$\begin{matrix}{z_{W}^{C_{k}} = \frac{\left( p_{AC_{k}}^{\mathcal{G}} \right)^{T} \cdot p_{{CW}_{k}}^{\mathcal{G}}}{p_{{AC}_{k}}^{\mathcal{G}}}} & (20) \\{y_{W}^{C_{k}} = 0} & (21) \\{x_{W}^{C_{k}} = \sqrt{{p_{{CW}_{k}}^{\mathcal{G}}}^{2} - \left( z_{W}^{C_{k}} \right)^{2}}} & (22)\end{matrix}$

Next, the coordinates of W are transformed to the local frames of everycoil, that is, p_(W) ^(C) ^(k) =

is obtained. Then, by utilizing the established field map of a singlecoil, Equation (23) is obtained:

$\begin{matrix}{{{\overset{\_}{h}}_{k}^{C_{k}}\left( p_{W}^{C_{k}} \right)} = {\left\lbrack {{\overset{\_}{h}}_{kx}^{C_{k}}{\overset{\_}{h}}_{ky}^{C_{k}}{\overset{\_}{h}}_{kz}^{C_{k}}} \right\rbrack^{T} = \begin{bmatrix}{{{\Phi_{norm}\left( {x_{W}^{C_{k}},z_{W}^{C_{k}}} \right)} \cdot \sin}\;\left( {\Phi_{\beta}\left( {x_{W}^{C_{k}},z_{W}^{C_{k}}} \right)} \right)} \\0 \\{{{\Phi_{norm}\left( {x_{W}^{C_{k}},z_{W}^{C_{k}}} \right)} \cdot \cos}\;\left( {\Phi_{\beta}\left( {x_{W}^{C_{k}},z_{W}^{C_{k}}} \right)} \right)}\end{bmatrix}}} & (23)\end{matrix}$

The unit gradient matrix at coil local frames also can be obtained bysubstituting p_(W) ^(C) ^(k) into the unit map of gradient matrices.Simplified by the cylindrical coil and the establishment method of thelocal frames, the unit gradient matrix becomes Equation (24):

$\begin{matrix}{{{{\overset{\_}{G}}_{k}^{C_{k}}\left( p_{W}^{C_{k}} \right)} = \begin{bmatrix}\frac{\partial{{\overset{\_}{\mathcal{M}}}_{x}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial x^{\mathcal{C}_{k}}} & 0 & \frac{\partial{{\overset{\_}{\mathcal{M}}}_{x}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial z^{\mathcal{C}_{k}}} \\0 & \frac{\partial{{\overset{\_}{\mathcal{M}}}_{y}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial y^{\mathcal{C}_{k}}} & 0 \\\frac{\partial{{\overset{\_}{\mathcal{M}}}_{x}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial z^{\mathcal{C}_{k}}} & 0 & \frac{\partial{{\overset{\_}{\mathcal{M}}}_{z}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial z^{\mathcal{C}_{k}}}\end{bmatrix}}{{{where}\mspace{14mu}\frac{\partial{{\overset{\_}{\mathcal{M}}}_{z}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial z^{\mathcal{C}_{k}}}} = {- {\left( {\frac{\partial{{\overset{\_}{\mathcal{M}}}_{y}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial y^{\mathcal{C}_{k}}} + \frac{\partial{{\overset{\_}{\mathcal{M}}}_{x}^{\mathcal{C}_{k}}\left( p_{W}^{\mathcal{C}_{k}} \right)}}{\partial x^{\mathcal{C}_{k}}}} \right).}}}} & (24)\end{matrix}$

To transform the obtained magnetic field and field gradient matrix tothe global frame for superposition calculation, the rotation matrix

is derived. For this purpose, the following relationship as shown inEquation (25) is utilized:

[

]=

·[{circumflex over (x)} ^(C) ^(k) ŷ ^(C) ^(k) {circumflex over (z)} ^(C)^(k) ]  (25)

where

is the global-frame coordinate of the x axis of the local frame of thek-th coil, then

=[

]·[{circumflex over (x)} ^(C) ^(k) ŷ ^(C) ^(k) {circumflex over (z)}^(C) ^(k) ]⁻¹  (26)

Since

$\begin{matrix}{\left\lbrack {{\hat{x}}^{C_{k}}{\hat{y}}^{C_{k}}{\hat{z}}^{C_{k}}} \right\rbrack = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}} & (27)\end{matrix}$thus,

=[

]  (28)

where

and

are sequentially obtained by

$\begin{matrix}{{\hat{z}}_{C_{k}}^{\mathcal{G}} = {{\hat{p}}_{AC_{k}}^{\mathcal{G}} = \frac{{\hat{p}}_{AC_{k}}^{\mathcal{G}}}{p_{AC_{k}}^{\mathcal{G}}}}} & (29) \\{{\hat{x}}_{C_{k}}^{\mathcal{G}} = {{\hat{p}}_{{CW}_{k}}^{\mathcal{G}} - {\left( {\hat{p}}_{{CW}_{k}}^{\mathcal{G}} \right)^{T} \cdot p_{AC_{k}}^{\mathcal{G}} \cdot p_{AC_{k}}^{\mathcal{G}}}}} & (30) \\{{\hat{y}}_{C_{k}}^{\mathcal{G}} = {{\hat{z}}_{C_{k}}^{\mathcal{G}} \times {\hat{x}}_{C_{k}}^{\mathcal{G}}}} & (31)\end{matrix}$

With

being obtained, magnetic forces of every coil at the global frame can bereadily calculated using Equations (7) and (8). After the magnetic fieldand force vectors of every coil are transformed to the global coordinateframe, the optimal coil currents to generate the desired field and forcecan be calculated by Equations (6) and (10).

FIGS. 3A-3B show the unit field maps of the mobile parallelelectromagnetic coils. In particular, FIG. 3A shows the finite elementmethod (FEM) data of the coils, where the local frame {O_(c)−{circumflexover (x)}^(c)ŷ^(c){circumflex over (z)}^(c)} is defined for the fieldcomputation. For different mobile parallel electromagnetic coils, O^(c)^(k) coincides with C_(k) in the global coordinate system. FIG. 3B showsthe comparison of the calibrated model with the FEM data andexperimental data.

The magnetic manipulation system comprises a framework of a fieldmapping for a general coil and 3D field mapping for the whole system. Aneural network is included to calibrate the FEM data in the field mapdomain of the coil since neural networks have the capability toapproximate any nonlinear functions with arbitrary accuracy in finitedefinition domain. FIG. 3A illustrates the coils of FIG. 1 which has adimension of φ30 mm×125 mm. Its large length-to-diameter ratio (>4),large field map domain and short distance between the coils and fieldmap domain hinder the usage of the dipole model.

For the neural network-based calibration method, COMSOL Multiphysics 5.3of COMSOL Inc., Burlington, USA is first used to create the FEM of thecoils as shown in FIG. 3A. Because the coils are axisymmetric, a 2Dsimulation is sufficient for establishing the 3D field map. A localreference frame {

} is constructed to compute the magnetic field at any position in thefield map domain of a coil. Then, two 9×11 data matrices−Φ_(norm)(x^(c), z^(c)) and −Φ_(β)(x^(c), z^(c)) (x^(c)∈{−50, −40, . . ., 40, 50}, z^(c)∈{20, 30, . . . , 120, 130}) are acquired from the FEMdata corresponding to the norm and angle of the magnetic field vector,when the coil is excited by currents of about 1 Amp. Definition of theangle β is illustrated in FIG. 3A. Third, the real magnetic fieldvectors at the data points are experimentally measured with a 3Dmagnetic field sensor (for example, Model: TLE493D W22B6, InfineonInc.). In order to reduce the error of the FEM-based model, calibrationis conducted utilizing the experimental measurement. A three-layerneural network is constructed for the calibration purpose. Its inputsare the coordinates and the corresponding field from simulation, and itsoutput is the calibrated field based on the same coordinates. Aftertraining the neural network using the aforementioned simulation andexperimental data, additional 8×10 data (x^(c)∈{−45, −35, . . . , 35,45}, z^(c)∈{25, 35, . . . , 115, 125}) are used to evaluate this method.Results plotted in FIG. 3B show that the calibration method reduces themean error and standard deviation. After obtaining the 3D field map, thegradient matrix can be calculated by taking derivatives of the field mapby Equation (3).

FIG. 4 shows the representation of the plane expanded by the symmetryaxis of the workspace and the k^(th) sliding track. Sliding track asshown in FIG. 1 is one of the actuators that drive the parallelmechanism. Other devices, for example, a ball screw table, rotationaljoints, can also be used as long as they can fulfill the requirement ofthe mechanical structure. The superscripts ‘′’ and ‘″’ represents twoextreme positions where ϕ has its smallest and largest values,respectively. {L_(max)} and {L_(min)} represent two special cases that Lhas its maximum and minimum allowed values, respectively. The design ofthe magnetic manipulation system begins with the workspace which ishighlighted in purple in FIG. 4. Considering the axis symmetry of thesystem, the desired workspace is taken as a cylinder with a radius ofR_(W) and a height of H_(W). Indicated by Equation (12), the systemkinematics can be classified to two categories. As shown in FIG. 4, abottom center

of the workspace is located on the symmetry axis of the work space. InFIG. 4, the methodology of branch design is deduced for 0°≤θ≤45°, whichcan be easily extended to the other category.

The objective of the mechanical design is to ensure that there are nosingularities for the kinematics of the parallel mechanism and the fieldgeneration, at the same time, the overall system can be as compact aspossible. ϕ is defined as the intersection angle between the coil branchand its sliding track as shown in FIG. 4. Due to the linear actuationmechanism used in this embodiment, the intersection angle between thecoil branch and its sliding track is evaluated to inhibit structuralsingularities. It can be deduced that ϕ has its extreme values, thesmallest value ϕ′ and the largest value ϕ″ for the whole workspace inthis plane. In other embodiments of the invention, however, therelationship between structural linkage and actuation mechanism can beevaluated by other parameters.

In order to inhibit singularities of the parallel mechanism, each coilbranch is disposed not to be perpendicular to its sliding track. Inaddition, the coil branch also cannot be in parallel to its slidingtrack due to the mechanical constraint. Therefore, the extreme values ofϕ satisfy Equation (32):

$\begin{matrix}{{\phi^{\prime} \geq \phi_{\min} \geq {0{^\circ}}}{\phi^{''} \leq \phi_{\max} \leq {90{^\circ}}}} & (32)\end{matrix}$

where ϕ_(min) and ϕ_(max) are flexibly determined constants.

To make a tradeoff between the minimal radius of the overall systemR_(o) and the sufficient space for hardware implementation, R_(o) isdefined by Equation (33):

R _(o)=1.5R _(w) +L _(MP)  (33)

According to FIG. 4, the horizontal coordinate of the bottom end of thesliding track equals R_(o). To suppress the overall height of theoverall system Ho, vertical coordinate of the bottom end of each slidingtrack H_(t) is to be minimized. This value is obtained when ϕ″ reachesϕ_(max), based on Equation (34):

$\begin{matrix}{H_{t} = \frac{R_{o} + R_{w} - L_{MP}}{\tan\left( {\Phi_{\max} - \theta} \right)}} & (34)\end{matrix}$

After positions of the sliding tracks being obtained, the length of thecoil branch L is the only undetermined structural parameter.Optimization is utilized to solve the length of L. First, theoptimization domain (L_(min), L_(max)) is deduced. As shown in FIG. 4,if Φ″ equals Φ_(max), the coil branch length has its allowed minimumvalue L_(min) which can be calculated by Equation (35):

$\begin{matrix}{L_{\min} = \frac{R_{o} + R_{w} - L_{MP}}{\sin\left( {\Phi_{\max} - \theta} \right)}} & (35)\end{matrix}$

Similarly, L has its allowed maximum value L_(max) when Φ″ equalsΦ_(max). By Sine theorem, L_(max) is calculated by Equation (36)

$\begin{matrix}{L_{\max} = \frac{\left( {R_{o} - R_{w} - L_{MP} - {\Delta H\tan\;\theta}} \right){\sin\left( {{90{^\circ}} - \theta} \right)}}{\sin\Phi_{\min}}} & (36) \\{where} & \; \\{{\Delta\; H} = {H_{w} - \frac{R_{o} + R_{w} - L_{MP}}{\tan\left( {\Phi_{\max} - \theta} \right)}}} & (37)\end{matrix}$

The maximum available H_(w) can be obtained by system constrains: (1)L_(max)>L_(min) (2) A_(k)′ does not coincide with the symmetry axis ofthe system, i.e. L_(max) sin (θ−Φ_(min))<R_(w)+L_(MP). Let H_(w1) andH_(w2) be the solutions of L_(max)=L_(min) and L_(max) sin(θ−Φ_(min))<R_(w)+L_(MP), respectively, then H_(w) satisfies formula(38):

H _(w)<min(H _(w1) ,H _(w2))  (38)

H_(w1) is omitted if θ=0, under which condition L_(max) is larger thanL_(min) for any H_(w). H_(w2) is omitted if θ≤ϕ_(min) since, in thiscase, A_(k)′ will not coincide with the symmetry axis of the system.Apparently, a larger Hw leads to a smaller range [L_(min), L_(max)].

Performance metrics are required to derive the optimal L. Both motionactuation capability and the field generation capability are taken intoconsideration in order to optimize the length L. For the motionactuation performance, by the above parameter design, the parallelmechanism is guaranteed to have no singularity, but its kinematicsproperty is considered to optimally choose L. To this end, for aspecific L, the Jacobian matrix of the parallel mechanism J_(m) isderived as follows. Substitute Equations (8) and (10) into Equation(11), then Equation (39) is obtained:

$\begin{matrix}{{\left( {x_{p} - x_{k}} \right)^{2} + \left( {y_{p} - y_{k}} \right)^{2} + \left( {z_{p} - z_{k}} \right)^{2}} = L} & (39) \\{where} & \; \\\left\{ \begin{matrix}{x_{k} = {{\left( {L_{h} + {q_{k}\sin\theta}} \right)\cos\;\alpha_{k}} - {L_{MP}\cos\;\alpha_{k}}}} \\{y_{k} = {{\left( {L_{h} + {q_{k}\sin\theta}} \right)\sin\;\alpha_{k}} - {L_{MP}\sin\;\alpha_{k}}}} \\{z_{k} = {L_{V} - {q_{k}\cos\theta}}}\end{matrix} \right. & (40)\end{matrix}$

L_(h) and L_(V) are expressed by

$\begin{matrix}\left\{ \begin{matrix}{L_{h} = {R_{w} + L_{MP} - {L\;\sin\;\left( {\theta - \phi^{\prime}} \right)}}} \\{L_{V} = {H_{o} = {H_{W} + {L\cos\;\left( {\theta - \phi^{\prime}} \right)}}}}\end{matrix} \right. & (41)\end{matrix}$

Where ϕ′ is calculated by Equation (42):

$\begin{matrix}{\phi^{\prime} = {\arcsin\left( \frac{\left( {R_{o} - R_{w} - L_{MP} - {\Delta H\tan\;\theta}} \right){\sin\left( {{90{^\circ}} - \theta} \right)}}{L} \right)}} & (42)\end{matrix}$

Differentiating Equation (39) with respect to time leads to Equation(43):

(x _(p) −x _(k)){dot over (x)} _(p)+(y _(p) −y _(k)){dot over (y)}_(p)+(z _(p) −z _(k))ż _(p) =D _(k) {dot over (q)} _(k)  (43)

Where

D _(k)=(x _(p) −x _(k)) sin θ cos α_(k)+(y _(p) −y _(k)) sin θ sinα_(k)−(z _(p) −z _(k)) cos θ  (44)

Equation (39) is rearranged to obtain Equation (45):

{dot over (q)}=

  (45)

The Jacobian matrix is shown by Equation (46):

$\begin{matrix}{J_{m} = \begin{bmatrix}\frac{x_{P} - x_{1}}{D_{1}} & \frac{y_{P} - y_{1}}{D_{1}} & \frac{z_{P} - z_{1}}{D_{1}} \\\frac{x_{P} - x_{2}}{D_{2}} & \frac{y_{P} - y_{2}}{D_{2}} & \frac{z_{P} - z_{2}}{D_{2}} \\\vdots & \vdots & \vdots \\\frac{x_{P} - x_{k}}{D_{k}} & \frac{y_{P} - y_{k}}{D_{k}} & \frac{z_{P} - z_{k}}{D_{k}}\end{bmatrix}} & (46)\end{matrix}$

The reciprocal of the condition number of J_(m) is selected as theperformance metrics for the motion actuation as shown in Equation (47):

$\begin{matrix}{\mu_{m} = \frac{1}{\kappa_{m}}} & (47)\end{matrix}$

where κ_(m)=∥J_(m) ^(†)∥·∥J_(m)∥ and ∥·∥ denotes the second norm of thematrix. μ_(m) has a value range of [0,1] that reflects the distance tothe actuation singularity. μ_(m)=0 indicates that the parallel mechanismenters its singularity so that it is out of control. On the contrary,the larger the μ_(m) is, the farther the distance to singularities isand the more isotropic actuation capability is. Although μ_(m) is only alocal index, its average—AVG (μ_(m)) and minimum MIN (μ_(m)) can be usedover the whole workspace to evaluate the overall system performance.

In a similar manner, the field generation performance can be evaluated.Different from the mechanical mechanism, coil currents can be controlledto be at an arbitrarily high speed. Therefore, instead of consideringthe kinematics, the properties of Ĥ^(†) in Equation (6) can be directlyused for the performance evaluation of AVG (μ_(h)) and minimum MIN(μ_(h)), in which

$\begin{matrix}{\mu_{h} = {{\frac{1}{\kappa_{h}}\mspace{14mu}{and}\mspace{14mu}\kappa_{h}} = {{{\hat{H}}^{\dagger}} \cdot {{\hat{H}}.}}}} & (48)\end{matrix}$

The method to quantify the overall system performance is to construct acomposite performance metrics Q as shown by Equation (49)

Q=W ₁·AVG(μ_(m))+W ₂·MIN(μ_(m))+W ₃·AVG(μ_(h))+W ₄·MIN(μ_(h))  (49)

where W₁ to W₄ are constant weights.

This optimal coil branch length L_(opt) that results in the largest Qcan be found by offline simulations, after which the correspondingϕ_(opt)′ and ϕ_(opt)″ are obtained by substituting L_(opt) into Equation(42) and Equation (50), respectively.

$\begin{matrix}{\phi_{opt}^{''} = {\arcsin\left( \frac{L_{\min}{\sin\left( {{180{^\circ}} - \phi^{\prime}} \right)}}{L_{opt}} \right)}} & (50)\end{matrix}$

The necessary length of the sliding track L_(st) is readily computed byEquation (51):

$\begin{matrix}{L_{st} = {\frac{\left( {R_{o} - R_{w} - L_{MP} - {\Delta H\tan\;\theta}} \right){\sin\left( {{90{^\circ}} + \theta - \phi_{opt}^{\prime}} \right)}}{\sin\left( \phi_{opt}^{\prime} \right)} + \frac{\Delta H}{\cos\;\theta} - \frac{L_{\min}{\sin\left( {\phi_{\max} - \phi_{opt}^{''}} \right)}}{\sin\;\phi_{opt}^{''}}}} & (51)\end{matrix}$

With the established methodology, embodiments of the invention can bedesigned and constructed to show the manipulation of magnetic devicesusing multiple mobile coils.

FIG. 5 depicts the performance simulations for an embodiment of theinvention having different coil branch lengths. For each L from L_(min)to L_(max), μ_(m) and μ_(h) are computed with 12010 sample points forAVG (μ_(m)), AVG (μ_(h)), MIN (μ_(m)) and MIN (μ_(h)). In addition, fivep_(PW) shown in FIG. 7 are also computed for AVG (μ_(h)) and MIN(μ_(h)). The composite performance metric Q used to determine theoptimal L is computed by Equation (49).

Based on the optimization results, the optimal link length L_(opt) canbe obtained. With the required workspace radius (H_(w1) and H_(w2))being confirmed, the total height H_(w) can be determined. In order toaccommodate the magnetic coils in the structure of the parallelmechanism, the coil length has to be smaller than the diameter of theworkspace. The coils used here have predetermined diameters and lengthsand are equipped with soft iron cores. The coils have largelength-to-diameter ratio and their magnetic fields can be accuratelymodelled by the method mentioned above. Then the relevant key parameterscan be directly computed by the method discussed above.

FIGS. 6A-6B show the performance metrics in the whole workspace. Due tothe system symmetry, simulations are conducted for one third of thecylindrical workspace. μ_(m) is the evaluation parameter of the motionmetrics and μ_(h) is the evaluation parameter of the magnetic fieldgeneration. In particular, FIG. 6A shows the distributions of thekinematics metric for three coil branch lengths which are near L_(min),L_(opt) and L_(max), respectively. FIG. 6B shows the distributions ofthe field generation metric for the three coil branch lengths. Theshorter the L is, the more nonuniform the μ_(m) distribution becomes.According to FIG. 6B, the distribution of μ_(h) becomes irregular due tothe nonlinearities of the kinematics of the parallel mechanism and thefield distribution of the coils. At some locations, μ_(h) has very smallvalues near 0.1 when L is close to L_(min) or L_(max). This issue can beinhibited by optimizations.

FIG. 7 illustrates the visualization of μ_(h) in the workspace for sixdifferent p_(PW). Results demonstrate that although there are nosingularities, the field generation performance decreases for eachworking position when p_(PW) is increased, indicating that compared toconventional stationary coil systems, the magnetic manipulation andnavigation system of the embodiments of the subject invention keep asclose as possible to the manipulated devices, by which the fieldgeneration performance is maximized.

FIG. 8A illustrates the mechanical design of the embodiment of theinvention including the coil branch and the coil-end plate. Structuralmaterials utilized by the system have negligible magnetic permittivity.To constrain the pose of the coil-end plate to be invariant, each coilbranch has a parallelogram mechanism realized by the slider, thecoil-end plate and two linkages (Linkage I) with four spherical jointsfor linking them as shown in FIG. 8A. The coil is integrated into theparallelogram mechanism via two spherical joints, a linkage (Linkage II)and a connector. By this embodiment, the coil branch contains twoidentical parallelogram mechanisms that ensure the required 3D motion ofthe coil-end plate. A spring is utilized between the connector andLinkage II so that this mechanism is robust to the fabrication error.Synchronous belts are used to actuate the sliders in the embodiment. Forother embodiments, alternative rigid actuators (for example, aball-screw mechanism or the linear motors) can be employed.

FIG. 8B shows the design of coil-end plate. The distance between the twospherical joints of the two Linkages I (D_(lc)) are carefully selectedto inhibit collision between the coil and the two Linkages I. As aresult, the minimum distance between the two Linkages I is required tobe larger than the coil diameter. Derived from the geometricrelationship, this requirement is equivalent to formula (52):

$\begin{matrix}{D_{lc} > {\frac{2R_{c}L_{opt}}{\sqrt{L_{opt}^{2} - R_{w}^{2}}} + {2R_{1}}}} & (52)\end{matrix}$

where R_(c) and R₁ are the radius of the coil and Linkage I,respectively. On the other hand, the distance between the coil-end planeand the coil-end plate ensure that the two do not collide, when formula(53) is satisfied:

$\begin{matrix}{D_{ec} > {\frac{R_{c}w}{\sqrt{L_{opt}^{2} - R_{w}^{2}}} + D_{r}}} & (53)\end{matrix}$

where D_(r) stands for the distance from the spherical joint shaft tothe surface of the coil-end plate as shown in FIG. 8B. The value ofL_(MP) has to be large enough to ensure the coil branches does notcollide with each other based on the formula (54):

$\begin{matrix}{L_{MP} > \frac{{D_{lc}/2} + {\Delta D}}{\tan\left( \frac{360{^\circ}}{2K} \right)}} & (54)\end{matrix}$

where ΔD is the distance required to mount the Linkage I as shown inFIG. 8B.

In order to inhibit the magnetization of the mechanical structures thatwould influence the magnetic field of the coils, structural materialshaving negligible magnetic permittivity is used. For example, thecoil-end plate is fabricated by aluminum alloy and linkages are made of304 steel.

FIG. 8C illustrates the design of the interchangeable instrument module.The coil-end plate is customized for installing various 3D locationsensors or medical imaging devices. The embodiment shown in FIG. 8C issquared-hollow in the middle where instrument can be installed.Depending on the 3D location feedback methods applied for the close loopcontrol, instruments such as 3D ultrasonic array probe, 3 axis magneticlocation module and stereo camera can be applied. Location methods ofthe system can be adjusted according to the requirement of the task.

Vision based feedback can be used as a valid location method when thecontrolled objects are captured by cameras. A stereo camera can send 3Dlocation information to the control system. Because of the eye-in-handconfiguration of the system, large area vision-based tracking of thecontrolled object in transparent body can be achieved.

Ultrasound imaging system can be integrated as a sensing tool tofeedback the location of controlled object. Such location method can beused when the controlled objects are in animal or human body. Under suchcondition, cameras cannot capture the image of the controlled objectsand thus vision-based location feedback is not available. A 2D/3Dultrasound sensor can be installed on the coil-end plate. Localizing andtracking of the controlled objects is realized by analyzing theresulting images.

Magnetic localization is a valid localization method for trackingcontrolled. By implanting magnetic sensors on the coil-end plate, 3Dmagnetic sensors can detect the magnetic objects in the body. Same asultrasound imaging system, magnetic localization method can be used incontrolling objects in a body where the controlled target cannot becaptured by the cameras.

Different localization tools can be encapsulated as a sensing moduleindividually and can be respectively installed under differentrequirements. The coil-end plate is designed as an instrument platformwhere various kinds of 3D location sensors can be integrated.

FIG. 9 is a block diagram of the magnetic manipulation system comprisingthe mechanical system, the coil actuation and control module, the motoractuation and control module, and the host computer, as well as thesignaling relationships among them. In the embodiment, the parallel coilmechanism is driven by stepper motors via synchronous linear actuators.A power supply is adopted for power delivery. Each motor is sufficientfor moving the coil branches. When receiving the updated positions ofthe coil-end plate, a microcontroller computes the inverse kinematics ofthe parallel mechanism and generates control signals to the motoractuators to control the motion of the motors. A stereo cameracomprising two micro-endoscopes is installed on the coil-end plate totrack the 3D position of the controlled device for feedback control.Owing to the ‘camera-in-hand’ configuration, the magnetic manipulationsystem can integrate with high-resolution and narrow field-of-viewsensors for precise control task in a large workspace. Other embodimentscan use other 3D position sensors for feedback control. Movement of thecoil-end plate is performed by the methods implemented in the hostcomputer in real time based on the feedback position of the controlleddevice. Serial communication is implemented to send commands to themicrocontroller and receive the current position as feedback.

Each of the coils is driven by a servo-amplifier. Their power isdelivered by a direct current (DC) power supply assisted by the signalprocessing and control methods, the computer calculates the desired 3Dmagnetic field in real time based on the feedback positions of thecoil-end plate and the controlled device, and the proposed fieldgeneration method is also implemented on the host computer which thengenerates desired electric currents for the coils. The digital controlsignal is converted to analog control voltages and sent to the servoamplifiers through a multifunctional I/O card. Dynamic coil currents aregenerated by the three servo amplifiers in a closed-loop manner tooutput the desired magnetic field.

The experimental results of the field generation at three selectedmechanism poses are shown in FIGS. 10A-C, respectively. p_(PW) is keptstatic for all the poses. The reference fields for each pose are set ascircular rotating fields at XY, YZ and XZ planes as shown in FIGS.10D-10F, which can reflect the field generation capability for anarbitrary direction. Overall, the embodiment of the system and fieldgeneration methods can generate accurate magnetic fields in a largeworkspace even with the variation of the coil poses and positions.

FIGS. 11A-F show the schematic drawings of some embodiments ofalternative actuation methods. In particular, FIGS. 11A-C illustrate theactuation methods using rotational joints and FIGS. 11D-11F illustratethe actuation method using a linear motor. There are trade-offs thatneed to be considered. Rotational joints are highly space-efficient andcan drive the systems moving relatively fast, but they cannot providesteady positioning due to the mechanical structure limits and motorlimits. Linear actuation, such as Ball screw tables, can provide highprecision and high revolution but they can hardly reach high speedmanipulation. In FIG. 4, φ is used to describe the relationship betweensliding track and links and define the singularity conditioncorrespondingly. When taking rotational joints into consideration, thecritical angles that define the singularity condition are γ₁ and γ₂ asshown in FIG. 11C. The critical angles are γ₁′ and γ₂′ in the situationshown in FIG. 11F, if linear actuation is utilized correspondingly.Variations of the parallel actuation methods do change the overalldesign pipeline of the robotic structures and all parallel actuationmethods are valid as long as they can fulfill the requirements of theapplication.

FIGS. 12A-12D show schematic drawings of the interchangeable coilassembly. In particular, FIG. 12A shows the exploded view of the coilassembly. A complete coil assembly includes a connection part, a core, acoil frame, a coil and a cooling unit. Connection can be flanges orscrew holes as shown in FIG. 12A. If an extruded core tip is applied,side connection as shown in FIG. 12B can be used. The side connectionmethod can give more space for the extruded core tip and decrease thedistance between core and the controlled object. A core can be insertedinto the coil frame and therefore different core material can beselected. The coil frame is a socket with two side flange connection.The utilization of the frame can decouple the core and the coil whichenables better flexibility. Due to the modulated design, any part of thecoil assembly can be substituted when the coil assembly needsmaintenance. As shown in FIGS. 12C-12D, the cooling unit comprises twoparts: the heat exchange unit and the temperature control unit. The heatexchange unit has a cooling cavity for circulation of the coolant and itis made of high thermal conductivity material. There are sensorsinstalled in the cooling cavity which is shown as orange blocks in FIG.12D, monitoring the temperature change. They feedback the temperaturesignal through signal ports to the host computer and achieve close loopcontrol of the coil temperature. The cooling control unit regulates thecooling effect and thus keeps the coil in a reliable working temperaturewindow. Overheating causes device failure and hazardous incidents. Thecooling system can elongate continuous working time of the system andprotect the user and the operator from potential harms.

FIGS. 13A-13D show certain alternative core tip shapes. Different coretip shapes generate different kinds of magnetic fields, each shapehaving its own advantages. Ordinary tip shape as shown in FIG. 13Agenerates medium strong magnetic field in medium range. Extruded shapeshown in FIG. 13B gives a stronger magnetic strength in a shorter rangeand the magnetic field degrades faster. Cone tip as shown in FIG. 13Ccan greatly concentrate very strong magnetic field in a small area. Thehalf-sphere tip as shown in FIG. 13D can generate more uniform magneticfield. The core tip can have many shapes which are not limited to theexamples shown in the FIGS. 13A-13D. Due to the interchangeable designof the coil assembly, core tip shape can be adjusted by changing thecore. The flexibility helps the system to meet various requirements.

FIGS. 14A-14B show the schematic drawing of an isolation plate forinhibiting heat and electricity. The distance sensors can send signalsback to the host computer to indicate the distance between the isolationplate and the body surface such that a method can be implemented toinhibit collision between the system and the body. The body in which thesystem controls the magnetic objects can be a human body or an animalbody. The isolation plate helps minimize the potential harm that thesystem can do to the body.

The present invention provides a magnetic manipulation and navigationsystem utilizing parallel-structured mobile electromagnetic coils formoving and navigating magnetic devices in a body.

The parallel mechanism precisely positions the electromagnetic coils totargeted locations and a control unit is configured to regulate thecurrents in the electromagnetic coils. The magnetic manipulation andnavigation system can manipulate a magnetic device in a large 3D workingarea in the vicinity of the body with a combination of robotic structureposition control and electromagnetic coil current control, inhibitingthe use of huge electromagnetic coils and superconductingelectromagnets.

At least three electromagnets with soft iron cores are installed on theparallel-structured linkage and these electromagnets connect to oneanother through a coil-end joint plate. The electromagnetic coils canmove to any location by actuating the parallel mechanism and the controlunit can adapt the coil currents to drive the electromagnetic coils togenerate specific dynamic magnetic field. Because of the movementcapability of the coils, a large 3D workspace is promised while thecoils can be kept in the vicinity of the controlled devices so that thescalability problems of coils are inhibited.

Owing to the special structure of the parallel mechanism, the coils canbe integrated as part of the robot structure. On one hand, theelectromagnetic coils that are compactly structured by the parallellinks have high stiffness when the parallel mechanism linkage is held instatic position. On the other hand, the parallel mechanism-structuredlinkages that connect each electromagnetic coil can be actuated to movethe electromagnetic coils to desired locations in the vicinity of thebody where the magnetic device locates.

Furthermore, the electromagnetic coils can move along a preferredtrajectory and the current running in the coils can be controlled togenerate desired magnetic fields when the magnetic manipulation andnavigation system is moving a magnetic element through the body.

Moreover, the workspace can be easily enlarged without requirements toupgrade the size of the coils and the ratio between the volume ofeffective workspace and the volume of the whole system is much higherthan the existing electromagnetic manipulation systems.

All patents, patent applications, provisional applications, andpublications referred to or cited herein are incorporated by referencein their entirety, including all figures and tables, to the extent theyare not inconsistent with the explicit teachings of this specification.

It should be understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication. In addition, any elements or limitations of any inventionor embodiment thereof disclosed herein can be combined with any and/orall other elements or limitations (individually or in any combination)or any other invention or embodiment thereof disclosed herein, and allsuch combinations are contemplated with the scope of the inventionwithout limitation thereto.

REFERENCES

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1. A magnetic manipulation system having mobile coils for moving andnavigating a magnetic device in a body, comprising: a robotic parallelmechanism comprising at least three electromagnets and at least threeelectromagnetic coils coupled to the at least three electromagnets,respectively, wherein the electromagnetic coils are actuated to keep theelectromagnets in static conditions or move the electromagnets along adesired trajectory; a current control unit supplying currents to theelectromagnetic coils, the electromagnetic coils having soft iron cores,wherein the currents supplied by the control unit are configured togenerate a dynamic magnetic field in a linear region of each soft ironcore, wherein the current control unit and the robotic parallelmechanism are configured to generate desired dynamic magnetic fields indesired positions within a workspace to control a magnetic device; and athree-dimensional (3D) position sensor configured for performing a closeloop control of the robotic parallel mechanism.
 2. The magneticmanipulation system of claim 1, further comprising a coil-end jointplate, actuation units, and structural linkages that connect thecoil-end joint plate to the robotic parallel mechanism.
 3. The magneticmanipulation system of claim 2, wherein the coil-end joint plate has aplurality of sides corresponding to a plurality of branches of eachelectromagnetic coil, and wherein instruments are mounted on thecoil-end joint plate and the coil-end joint plate is connected to alower end of each electromagnetic coil.
 4. The magnetic manipulationsystem of claim 2, wherein the robotic parallel mechanism is anactuation mechanism having K branches including linear actuationmechanisms and rotational actuation mechanisms, wherein K is an integergreater than zero, and wherein the rotational actuation mechanismsinclude motors and gears, motors and belts, or motors and linkages, andwherein the linear actuation mechanisms include ball screw tables,sliding tracks, and pneumatic actuation.
 5. The magnetic manipulationsystem of claim 2, wherein the robotic parallel mechanism is made of lowmagnetic permittivity materials including aluminum and 304 steel.
 6. Themagnetic manipulation system of claim 2, wherein a position of a centerof the coil-end joint plate has a deterministic relationship withactuator positions of the robotic parallel mechanism while anorientation of the coil-end joint plate is constrained by the roboticparallel mechanisms to be invariant.
 7. The magnetic manipulation systemof claim 2, the coil-end joint plate is configured to install one ormore instruments selected from 3D ultrasonic probes, 3D magnetic sensorsor stereo cameras, the 3D ultrasonic probes, the 3D magnetic sensors,and the stereo cameras being modulated and interchangeable.
 8. Themagnetic manipulation system of claim 7, wherein a 3D location method isconfigured to conduct close loop control of a plurality of magneticobjects, and wherein the 3D location method includes one or moreselected from ultrasonic imaging, magnetic localization, andvision-based localization method, depending on the instruments installedon the coil-end joint plate.
 9. The magnetic manipulation system ofclaim 2, wherein the electromagnetic coils are connected to the coil-endjoint plate by universal joints, and wherein the electromagnetic coilsmove and are aligned with the structural linkages.
 10. A method of amagnetic manipulation system having mobile electromagnetic coils formoving and navigating a magnetic device in a body wherein the methoddetermines parameters of the magnetic manipulation system to keep themagnetic manipulation system as compact as possible and inhibit anysingularities with respect to kinematics and field generation, themethod comprising: analyzing a workspace of the magnetic manipulationsystem; determining spatial relationships between coil branches of themagnetic manipulation system and actuation mechanisms of the coilbranches; and determining optimal link length of the coil branches. 11.The method of claim 10, further comprising optimizing for deriving theoptimal link length, wherein performance metrics for motion actuationand field generation are evaluated based on a condition number of theperformance metrics.
 12. The method of claim 10, wherein the workspaceis axis-symmetric and a bottom center of the workspace is located on asymmetry axis of the workspace.
 13. The method of claim 10, wherein thespatial relationship between the coil branches and moving trajectoriesof the coil branches is delimited by the singularities and physicalconstraints of the magnetic manipulation system.
 14. The method of claim10, wherein the link length is optimized based on a minimum radius ofthe magnetic manipulation system and whether there is enough space forhardware implementation.
 15. The method of claim 10, further comprisingproviding a framework for calculating and controlling field generationof the coil branches of the magnetic manipulation system, wherein theframework includes a field map of one or more of the coil branches,inverse kinematics of the coil branches, and field computation andcontrol by dynamic coordinate transformation.
 16. The method of claim15, further comprising generating and calibrating a unit map of one ofthe coil branches; wherein the coil branches each has alength-to-diameter ratio greater than 3, a field map domain greater thantwice of a diameter of the corresponding coil branch, and a distancebetween the corresponding coil branch and the field map domain smallerthan one half of a length of the corresponding coil branch; wherein aneural network is configured to calibrate finite element data created bya simulation of the field map domain of the corresponding coil branch;and wherein real magnetic field vectors which are experimentallymeasured at data points are based on to calibrate a 3D magnetic fieldmap and magnetic field gradient.
 17. The method of claim 15, furthercomprising providing currents to the coil branches for generating adesired magnetic field, which comprises deriving the inverse kinematicsof the coil branches and field computing and controlling by the dynamiccoordinate transformation; wherein the magnetic field calculation andcalculation of the field superposition of the coil branches areperformed by the dynamic coordinate transformation and a unit map of oneof the coil branches; and wherein resulting magnetic field vectors andgradient matrices connect the currents to the coil branches that iscontrollable to a desired magnetic field.
 18. An interchangeable coilassembly, comprising: a core; a coil frame; and a coil; wherein the coilframe decouples the coil and the core, wherein the core, the coil frameor the coil is changeable when the other one fails, and whereindifferent core tips are configured to be inserted in the coil frame tomeet magnetic field requirements.
 19. The interchangeable coil assemblyof claim 18, further comprising a cooling unit for controllingtemperature of the coil, and a temperature control unit monitoring thecoil temperature through thermal sensors and regulating a heat exchangerate to keep the coil in a working condition and elongate continuousworking time of the interchangeable coil assembly.
 20. The magneticmanipulation system of claim 1, further comprising an isolation plateattached to the coil-end joint plate for controlling a distance betweenthe magnetic manipulation system and the body that includes magneticallycontrolled objects and integrates distance sensors and temperaturesensors to inhibit body collision and overheating.